Hudson Executive Investment Corp III (HIII) 10-Q 2022 Q2 Quarterly report

EXHIBIT 32.1

CERTIFICATION PURSUANT TO

18 U.S.C. SECTION 1350

AS ADOPTED PURSUANT TO

SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

In connection with the Quarterly Report of HUDSON EXECUTIVE INVESTMENT CORP. III (the “Company”) on Form 10-Q for the quarterly period ended June 30, 2022, as filed with the Securities and Exchange Commission (the “Report”), I, Douglas G. Bergeron, Chief Executive Officer of the Company, certify, pursuant to 18 U.S.C. §1350, as adopted pursuant to §906 of the Sarbanes-Oxley Act of 2002, that, to the best of my knowledge:

1. The Report fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934; and

2. The information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the company.

Dated: August 15, 2022

/s/ Douglas G Bergeron

Douglas G Bergeron

Chief Executive Officer

(Principal Executive Officer)